Results 1 to 10 of about 130 (120)

A new formula for the coefficients of Gaussian polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of ...
Andrica Dorin, Bagdasar Ovidiu
doaj   +1 more source

STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE

Forum of Mathematics, Pi, 2015
Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
doaj   +1 more source

Extended Genus Fields of Abelian Extensions of Rational Function Fields

Axioms
In this paper, we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. For the general case, we use the fact that the extended genus fields
Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador   +1 more
doaj   +1 more source

The Chromatic Fourier Transform

Forum of Mathematics, Pi
We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$ , as well as a certain duality for the $E_n$ -(co)homology of $\pi
Tobias Barthel, Shachar Carmeli, Tomer M. Schlank, Lior Yanovski   +3 more
doaj   +1 more source

Notes on Number Theory

Mathematics
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-
Miroslav Stoenchev, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source

Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381

Transactions on Cryptographic Hardware and Embedded Systems
Non-degenerate bilinear maps on elliptic curves, commonly referred to as pairings, have many applications including short signature schemes, zero-knowledge proofs and remote attestation protocols.
Hao Cheng, Georgios Fotiadis, Johann Großschädl, Daniel Page   +3 more
doaj   +1 more source

Abelian number fields with frobenian conditions

Mathematika, Volume 72, Issue 4, October 2026.
Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
wiley   +1 more source

Localization sequences for logarithmic topological cyclic homology

Journal of Topology, Volume 19, Issue 3, September 2026.
Abstract We introduce the notion of an Ek$\mathbb {E}_k$‐ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories. Our approach is based on Thom R$R$‐algebras.
John Rognes, Steffen Sagave, Christian Schlichtkrull   +2 more
wiley   +1 more source

A trace–path integral formula over function fields

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We show that an arithmetic path integral over the ℓ$\ell$‐torsion of a Jacobian J[ℓ]$J[\ell]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ])$H(J[\ell])$, up to an explicitly determined sign.
Yan Yau Cheng
wiley   +1 more source

Syntomic cohomology and real topological cyclic homology

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We define motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions of syntomic cohomology.
Doosung Park
wiley   +1 more source